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Tentukan integral x squared square root of x plus 1 end root

Pembahasan Soal:

integral x squared square root of x plus 1 end root

Untuk menyelesaikannya akan digunakan metode substitusi dengan membuat pemisalan.

Misal 

table attributes columnalign right center left columnspacing 0px end attributes row straight u equals cell square root of straight x plus 1 end root end cell row cell u squared end cell equals cell x plus 1 end cell row x equals cell u squared minus 1 end cell row cell d u end cell equals cell 1 half open parentheses x plus 1 close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent d x end cell row cell 2 space d u end cell equals cell open parentheses x plus 1 close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent d x end cell row cell d x end cell equals cell 2 d u square root of x plus 1 end root end cell row cell d x end cell equals cell 2 u space d u end cell end table

nilai dx akan disubstitusikan ke integral x squared square root of x plus 1 end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell integral straight x squared square root of straight x plus 1 end root dx end cell equals cell integral straight u space 2 xdu end cell row cell 2 straight x integral udu end cell equals cell 2 straight x open parentheses 1 half straight u to the power of 1 half end exponent close parentheses plus straight C end cell row blank equals cell xu to the power of 1 half end exponent plus straight C end cell row blank equals cell straight x open parentheses square root of straight x plus 1 end root close parentheses to the power of 1 half end exponent plus straight C end cell end table

Jadi, integral x squared square root of x plus 1 end root equals x open parentheses square root of x plus 1 end root close parentheses to the power of 1 half end exponent plus C

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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